Add the following rational expressions. $\dfrac{14}{y^2+47}+\dfrac{2y^2-7}{y^2+47}=$
We want to add two rational expressions whose denominators are equal. We can do this by adding the numerators and keeping the denominator the same. [Does this fit with how we add rational numbers?] $\begin{aligned} &\phantom{=}\dfrac{14}{y^2+47}+\dfrac{2y^2-7}{y^2+47} \\\\ &=\dfrac{(14)+(2y^2-7)}{y^2+47} \\\\ &=\dfrac{14+2y^2-7}{y^2+47} \\\\ &=\dfrac{2y^2+7}{y^2+47} \end{aligned}$ In conclusion, $\dfrac{14}{y^2+47}+\dfrac{2y^2-7}{y^2+47}=\dfrac{2y^2+7}{y^2+47}$